13

Part of 2014 BMT Spring

Problems(2)

area chasing with angle bisector 2014 BMT Team 13

Source:

ABC

be a triangle with

AB = 16

AC = 10

BC = 18

D

AB

4AD = AB

and let E be the foot of the angle bisector from

B

AC

P

be the intersection of

CD

BE

. Find the area of the quadrilateral

ADPE

geometryareasangle bisector

cylinder is inscribed within a sphere 2014 BMT Individual 13

Source:

A cylinder is inscribed within a sphere of radius 10 such that its volume is almost-half that of the sphere. If almost-half is defined such that the cylinder has volume

\frac12+\frac{1}{250}

times the sphere’s volume, find the sum of all possible heights for the cylinder.

geometryVolume3D geometryspherecylinder